Converting a Nested 2D Loop to 1D

On GPUs, a single 1D loop can be more efficient than a nested 2D loop for tasks like sampling a 2D window. Here’s how to sample a 3x3 window of offsets using a 1D loop.

Source Code

// Window size.
const int WindowSize = 3;
const int WindowHalf = WindowSize / 2; // Integer division.

// 1D loop to iterate over 3x3 window.
for (int i = 0; i < (WindowSize * WindowSize); i++)
{
   float2 XY = float2(i % WindowSize, i / WindowSize) - WindowHalf;
}

Example: 3x3 Window Offsets

i#		X		Y
0	-1 + (0 % 3)	-1	-1 + trunc(0 / 3)	-1
1	-1 + (1 % 3)	0	-1 + trunc(1 / 3)	-1
2	-1 + (2 % 3)	1	-1 + trunc(2 / 3)	-1
3	-1 + (3 % 3)	-1	-1 + trunc(3 / 3)	0
4	-1 + (4 % 3)	0	-1 + trunc(4 / 3)	0
5	-1 + (5 % 3)	1	-1 + trunc(5 / 3)	0
6	-1 + (6 % 3)	-1	-1 + trunc(6 / 3)	1
7	-1 + (7 % 3)	0	-1 + trunc(7 / 3)	1
8	-1 + (8 % 3)	1	-1 + trunc(8 / 3)	1